A176308 - OEIS

A176308

Integers n such that n and n^3+-1 are squarefree numbers.

6, 42, 66, 78, 102, 114, 138, 186, 210, 222, 258, 282, 318, 330, 354, 366, 390, 402, 438, 462, 498, 510, 534, 546, 642, 678, 690, 714, 762, 786, 798, 858, 870, 894, 906, 942, 966, 978, 1002, 1038, 1086, 1110, 1122, 1218, 1230, 1254, 1266, 1290, 1302, 1338

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OFFSET

1,1

COMMENTS

All the terms are divisible by 6 since if n == 1, 2, 4, or 5 (mod 6) then either n^3 - 1 or n^3 + 1 is divisible by 9, and if n == 3 (mod 6) then either n^3 - 1 or n^3 + 1 is divisible by 4. - Amiram Eldar, Oct 01 2019

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

6=2*3; 6^3-1=5*41; 6^3+1=7*31,..

MATHEMATICA

f[n_]:=SquareFreeQ[n]; lst={}; Do[If[f[n^3-1]&&f[n^3+1]&&f[n], AppendTo[lst, n]], {n, 3*6!}]; lst

PROG

(Magma) [k:k in [2..1400]| IsSquarefree(k) and IsSquarefree(k^3-1) and IsSquarefree(k^3+1)]; // Marius A. Burtea, Oct 01 2019

CROSSREFS

Cf. A005117.

Sequence in context: A292316 A329000 A329339 * A103763 A191764 A043896

Adjacent sequences: A176305 A176306 A176307 * A176309 A176310 A176311

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 14 2010

STATUS

approved